Upper bounds for Euclidean minima of algebraic number fields

Eva Bayer Fluckiger
2006
Article

Résumé

The aim of this paper is to give new upper bounds for Euclidean minima of algebraic number fields. In particular, to show that Minkowski's conjecture holds for the maximal totally real subfields of cyclotomic fields of prime power conductor.

Source officielle

https://infoscience.epfl.ch/record/277393?ln=fr

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Moments of the number of points in a bounded set for number field lattices

Maryna Viazovska, Nihar Prakash Gargava, Vlad Serban

We examine the moments of the number of lattice points in a fixed ball of volume

V

for lattices in Euclidean space which are modules over the ring of integers of a number field

K

. In particular, denoting by

ω_K

the number of roots of unity in

K

, we ...

arXiv2023

Upper bounds for Euclidean minima of algebraic number fields

K3 surfaces, cyclotomic polynomials and orthogonal groups

Lattice packings through division algebras

Moments of the number of points in a bounded set for number field lattices

K3 surfaces, cyclotomic polynomials and orthogonal groups

Lattice packings through division algebras

Moments of the number of points in a bounded set for number field lattices